1. Field of the Invention
This invention relates to a method of displaying a field of unit vectors.
2. Description of Related Art
Determination and interpretation of a spatially dispersed field of unit vectors is desirable in many disciplines. This vector field may represent an the direction of instantaneous fluid velocity in a plane intersecting a volume of flowing fluids. It may also represent stress and strain force directions in a solid, or current flow direction through a conductor. One specific important use crystals in materials science and geology. Microscopy, x-ray diffraction, and other techniques are used to obtain the orientation of each crystal structure to create a vector field. Electron backscattering diffraction patterns (EBSP) has also been used to obtain lattice orientation as described in "A Review of Automated Orientation Imaging Microscopy (OIM)" by Stuart I. Wright, Journal of Computer-Assisted Microscopy, Vol. 5, No. 3, 1993 ("Wright Review"). The techniques can produce large (several thousands) arrays of orientation data.
The lattice orientation is important in metallurgy in determining where several crystals, or grains share the same orientation. If there are large crystals sharing the same orientation, it may become prone to fracture between crystalline lattice layers.
In other areas, growth of a single crystal is important, and therefore the need to determine the crystal orientations is desirable.
Once the unit vector fields are acquired, they are displayed. The most common method of processing and visualizing this data in materials sciences is pole figures and inverse pole figures "Preferred Orientation in Deformed Metals and Tocks: An Introduction to Modern texture Analysis" by Hans-Rudolf Wenk, ed., Academic Press, 1985, p. 11 ("Wenk publication"). In this method, a single axis of the crystal is mapped to a unit sphere, with a mark being made on the unit sphere where the ray intersects the unit sphere. The unit sphere is projected onto a disk using stereographic or equal area projections. This way the orientations associated with orientation in the sample are represented by point in the disk. This type of display can be very difficult to interpret, since it is not clear which point on the surface corresponds to which intersection of the unit sphere.
Other methods of display were created in recent years that try to address the growth of data volume as described in "Orientation Mapping" by F. C. Frank, Met. Trans., 19A, (1988), 403; and "Review, Microtexture Determination By Electron Back-Scatter Diffraction" by D. J. Dingley, V. Randle, Journal of Material Sci. 27 1992, 4545-4566. A disadvantage of Frank's method is that it maps orientation to three dimensional space thus requiring stereograms to view the map. Frank's method utilizing special cubic symmetry of particular lattice structure reduces the total spherical space to 1/48 of its original size.
In the Wright Review ibid., there has also been attempts to employ color mapping to display different orientations but, the color mapping did not ensure that crystals of similar orientation are assigned similar colors.
Currently there is a need for a method of vector field display which allows fast and easy interpretation.